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Fermion localization on degenerate and critical branes

In this work we analyze the localization of fermions on degenerate and critical Bloch branes. This is done directly on physical coordinates, in constrast to some works that has been using conformal coordinates. We find the range of coupling constants of the interaction of fermions with the scalar fields that allow us to have normalizable fermion zero-mode localized on the brane on both, critical and degenerate Bloch branes. In the case of critical branes our results agree with those found in [Class. Quantum Grav. \textbf{27} (2010) 185001]. The results on fermion localization on degenerate Bloch branes are new. We also propose a coupling of fermions to the scalar fields which leads to localization of massless fermion on both sides of a double-brane.